Circumsphere Radius of Dodecahedron given Midsphere Radius Calculator

✖The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Dodecahedron [r_m]

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✖Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Dodecahedron given Midsphere Radius [r_c]

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Circumsphere Radius of Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Midsphere Radius of Dodecahedron/(3+sqrt(5))
r_c = sqrt(3)*(1+sqrt(5))*r_m/(3+sqrt(5))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Circumsphere Radius of Dodecahedron - (Measured in Meter) - Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.
Midsphere Radius of Dodecahedron - (Measured in Meter) - The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Dodecahedron: 13 Meter --> 13 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(3)*(1+sqrt(5))*r_m/(3+sqrt(5)) --> sqrt(3)*(1+sqrt(5))*13/(3+sqrt(5))

Evaluating ... ...

r_c = 13.9160615011505

STEP 3: Convert Result to Output's Unit

13.9160615011505 Meter --> No Conversion Required

FINAL ANSWER

13.9160615011505 ≈ 13.91606 Meter <-- Circumsphere Radius of Dodecahedron

(Calculation completed in 00.020 seconds)

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< Circumsphere Radius of Dodecahedron Calculators

Circumsphere Radius of Dodecahedron given Total Surface Area

LaTeX Go Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

Circumsphere Radius of Dodecahedron given Volume

LaTeX Go Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)

Circumsphere Radius of Dodecahedron

LaTeX Go Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4

Circumsphere Radius of Dodecahedron given Face Diagonal

LaTeX Go Circumsphere Radius of Dodecahedron = sqrt(3)/2*Face Diagonal of Dodecahedron

Circumsphere Radius of Dodecahedron given Midsphere Radius Formula

LaTeX Go

Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Midsphere Radius of Dodecahedron/(3+sqrt(5))
r_c = sqrt(3)*(1+sqrt(5))*r_m/(3+sqrt(5))

What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Circumsphere Radius of Dodecahedron given Midsphere Radius?

Circumsphere Radius of Dodecahedron given Midsphere Radius calculator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Midsphere Radius of Dodecahedron/(3+sqrt(5)) to calculate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using midsphere radius of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Circumsphere Radius of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (r_m) and hit the calculate button. Here is how the Circumsphere Radius of Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 13.91606 = sqrt(3)*(1+sqrt(5))*13/(3+sqrt(5)).

FAQ

What is Circumsphere Radius of Dodecahedron given Midsphere Radius?

The Circumsphere Radius of Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using midsphere radius of Dodecahedron and is represented as r_c = sqrt(3)*(1+sqrt(5))*r_m/(3+sqrt(5)) or Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Midsphere Radius of Dodecahedron/(3+sqrt(5)). The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

How to calculate Circumsphere Radius of Dodecahedron given Midsphere Radius?

The Circumsphere Radius of Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using midsphere radius of Dodecahedron is calculated using Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Midsphere Radius of Dodecahedron/(3+sqrt(5)). To calculate Circumsphere Radius of Dodecahedron given Midsphere Radius, you need Midsphere Radius of Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Circumsphere Radius of Dodecahedron?

In this formula, Circumsphere Radius of Dodecahedron uses Midsphere Radius of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4
Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Circumsphere Radius of Dodecahedron = sqrt(3)/2*Face Diagonal of Dodecahedron

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